Question

Find three cube roots of 64i

Answer 1

Express this in the form of a(cosx+isinx) first

Answer 2

4(cos+isinx) ?

Answer 3

I mean express 64i in the form of a(cosx+isinx)

Answer 4

\[
\sqrt[3]{64 i}=\sqrt[3]{64 e^{\frac{i \pi }{2}}}=\\4 e^{\frac{i \pi }{6}}=4
\left(\cos \left(\frac{\pi }{6}\right)+i \sin \left(\frac{\pi
}{6}\right)\right)=\\4 \left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)=2
\sqrt{3}+2 i
\]